[Physics] Physics Digest, Vol 21, Issue 9

[Tufail Abbas]

I have noted that James has raised attention to a very important aspect of
gravity,
Quote:  "Gravitic curvature happens in TWO dimensions only" and then he
raise objection,
Quote: " but -that- image has never been drawn or pictured"

I agree that a correct appreciation of meaning of dimensions in equations
of physics is very important.

As per definition, number of dimensions of a system, is the number of
independent coordinates points that must be used to describe the system. In
that sense, in response to Tom's query,  if 8 *intervals* represents
position along one dimension and 300000,000 *interval* represents position
on another dimension then (8, 300000000) is the complete 2-Dimensionsal
description of that system.

However in physical systems, the important question is what does a *unit
interval* along each of the dimensions represents:

a) Is the unit interval representation of some physically existing object?.
b)Or that *unit interval  *is representative of change in quantities of
physically existing object?
c) Or the *unit interval* just  represent a position on mathematical number
line without any relationship with physically existing objects? If this is
the case then dimension is just an abstraction, and not a physical
dimension.

Physically existing object is the object that occupies volume within a
finite boundary

So if we say that time is a *true physical dimension*, then it must occupy
a volume. And if time does not occupy any volume then it may qualify
as *mathematical
dimension*, but not as a *physical dimension*.

We should find out, what does mathematical equations of 4-D and above,
 represent in our 3-D realm. For example: Distance along curvilinear length
of helix of 3rd order in 3-D is similar to expression for linear distance
in 4-D coordinate system.  (
https://bigquestionsofuniverse.quora.com/Helix-of-Multiple-Order)



On Mon, 10 Dec 2018 at 20:52, carmam at tiscali.co.uk <carmam at tiscali.co.uk>
wrote:

> James, nobody else has asked, so I will. You mention "exponents as
> dimensions", yet an exponent (in maths) is quite simply shorthand for the
> number of zeros following a number, eg 3e8 is quite simply 300,000,000 , or
> the speed of light (rounded). Why is 3e8 a dimension when 300,000,000 is
> not?
>
> Tom Hollings
>
>
>
> ----Original Message----
> From: integrity at prodigy.net
> Date: 09/12/2018 20:17
> To: <physics at tuks.nl>
> Subj: Re: [Physics] Physics Digest, Vol 21, Issue 9
>
> Carl,
>
> Thanks for your gentle (and funny) chidings, and the interesting LaGrange
> points 'congregation' events description that are relevant.
>
> "Complex numbers" I don't see as a problem, since complex components, as I
> remember, are treated as another orthogonal 'dimension' when graphed.   I
> don't see any inconsistency or undefined dimension relations [or complex
> factors to be treated as 'non-dimensional'].
>
> Re gravity and the LaGrange points .. I totally agree with you.
> Absolutely related.   Mathematics and physics models - eg - all the
> conventional imagery of spacetime relativity as deformed elastic dimpled
> sheets (gravity 'wells' around masses) are misleading, stupid and absurd,
> according to the clean math equations as given by Newton -&- Einstein.  It
> was the only way to try and graphically show curvature of light paths
> through the 'distorted' spacetime of masses.  But think about it
> carefully.  A gravity-well dimple is a distortion in the z-dimension, out
> of the x,y plane.   I would be delighted if -anyone- can point to any
> gravity formula factors that go out of the x,y plane. (!)   None do.
> Gravitic curvature happens in TWO dimensions only .. but -that- image has
> never been drawn or pictured.
>
> Where I am going with those remarks, is that the same holds true for
> LaGrange points.  They exist in 2 dimensions not 3.  Now how can we
> identify such curvatures or fixed-loci .. using simpler relations
> concepts?   A modified understanding of 'dimensions' is what I propose.
>
> How? Why?   Well for starters, It began to occur to me when I was watch
> some Tokomak runs in 1965 at the Princeton Plasma Physics Lab.  It was my
> first exposure to the equipment involve with the experimentation.  Very
> large, very impressive .. all the energy and -massive- quantities of
> electron volts required to magnetically bottle, control, and contain ...
> for the -briefest- amount of time .. what simple few electrons do EASILY
> with comparatively -little- amount of electron volts.  Strange.  Very
> strange.  The universe accomplishes atoms formation (plasma confinement)
> naturally and easily ... everywhere ... versus the energy and conditions
> bring to bear to try and accomplish the same thing.
>
> The difference was glaring to me and it dawned on me that maybe some other
> important factor is involved .. which the universe embodies and uses, and
> which human intellect hadn't yet recognized as important, or present.
> Knowing that particle-pairs have a mathematical correspondence; knowing
> that atoms and waves exist in 3d~4d 'spaces' (by certain simple models) ..
> I posed myself a conjecture:  Maybe something else is involved that
> -balances- nuclear plasmas with the electron(s) forms and collectives?
> Something 'dimensional' .. whatever that might be (it was a starting
> question insight for me back then, not a developed model).  So I started
> exploring the masses ratio of proton to electron (simplest atom case) ..
> approx 1836:1.      After a few days, I found something interesting and
> close .. with a possible association to phasespace [where phasespace is
> appreciated as 3 momentum and 3 loci values  ; aka SIX dimensions (if a
> person is to be mathematically consistent in definition
> applications)].      1836 is interestingly close to 6(pi)^5 ; "six times pi
> to the fifth".
>
> Now, I had already started exploring the notion of exponent location
> values being representative of the continuum numberline .. that I mentioned
> in a previous post.   For example, under my hypothesis, the sample
> equations,  f(x) =  15 + 3x + (pi)x^2 + 109x^3 + x^4 ,  is unconventionally
> understood as an equation in 4 dimensions.  ['15' being a non-dimensional
> scalar value].
>
> To apply my hypothesis of "everything in math is (really) dimensional",
> the function is amendedly correctedly written:
>
> f(x) =  15x^0 + 3x^1 + (pi)x^2 + 109x^3 + x^4.       There are FIVE
> dimensional factors written, x^0, being the necessary foundational
> dimension involved.      Using that contention, 6(pi)^5, is a value in SIX
> dimensions .. which fits with phasespace interpretation.
>
> I haven't calculated other atoms Nuclear::electron cloud ratios, but the
> hydrogen atom proton::electron ratio suggests that something -dimensional-
> is necessarily "balanced", that holds atoms together.  Naturally and easily
> via the dimensional architecture of the universe, of phasespacetime.
>
> Back to gravity .. as 2 dimensional phenomena.    I don't understand
> anyone's complaints to the Einstein proposition that gravity is similar to
> acceleration events.    The accuracy is right there in his fundamental
> simplified equation "E=mc^2".  The problem is that neither Einstein, nor
> anyone after him, had the courage to explore the -meaning- of:  exponents
> as dimensions.  :-)
>
> Acceleration is (time x time).  t x t.   aka  t^2.    Right from the get
> go, Einstein had written that gravity is the resultant felt force of TWO
> -time dimensions- ... interacting:  c^2.     Apparently it has been
> difficult enough to grasp the notion that 'time' is a dimension, to take
> that next extra step that time could be architected as more than 'one'.
> [not just forward time and reverse time; but real orthogonal separate
> values].
>
> Yes, yes, yes.  I am conflating several relations here.  mass~energy
> equivalence as a relation of two time dimensions squared ; with a gravity
> field being the result of two time dimensions squared.   They are related
> .. which is why masses deform phasespacetime, and, phasespacetime
> co-affects masses.
>
> Now back to the misleading image of spacetime as an elastic deformed
> domain, in a third z-orthogonal direction.  The gravity field is more like
> a cross section of a magnetic field around a bar magnet:    Field lines are
> closer in certain locations and spread apart in others.  In other words:
> intensity densities are the correct image.   Which, can accurately be
> interpreted as density gradients.   Differential action potentials - across
> domains.      The great thing is that those GRADIENTS ... at next higher
> teirs of complexity and matter~energy forms (volumetric measures and
> densities in contained defined spaces ... which exhibit changes over time
> that the industrial revolution scientists understood as
> pressure/temperature/volume .. and then identified work potential and work
> accomplished .. aka actions enactable .. as the mysterious labels factor
> 'entropy') ... that, in my refreshed coordination of all those existential
> parameters ... "entropy" is a fundamental phenomena of changes over~across
> fields densities.  Thermodynamics is only one higher-order example of
> "entropy".   Unfortunately, our uber-engineering oriented society and
> scientists are fixed on thermodynamics as the only quality of entropy.
> Instead of dissecting the underlying relations ...  it tries to impose
> thermodynamics where it doesn't belong.  Gradients of all different sorts
> and states are 'entropy'.
>
> Distribution differences.    (same thing)   relocation changes  (same
> thing).  WHICH ...  :-)  ... is why Shannon and Weaver and von Neumann were
> accurate to ascribe entropy as a factor quality in 'Information Theory'.
>
> And, to 'pile on' with another interpretation that no one talks about or
> identifies:   CALCULUS ... based on the ability to recognize partitioning
> cuts (that reduce in size, and concurrently, quantity wise move towards
> infinity) .. what else is the capacity of a signal recognition system????
> ... except the ability to be fine-tuned enough to -recognize- a signal!
> Calculus was really the FIRST EXPLICIT "information theory" even though
> that label was never used.  Shannon's calculus based statistical based
> "information theory" is the SECOND information theory .. an IMPLICIT one
> that deals with recognition, and interpretation and noise.  For Leibnitz
> and Newton, 'noise' and non-data were not resident in defining the
> essential math relations in partitioning and infinities.
>
> Okay.  I'm sure I just inundated everyone with information overload.
> Ready over here ... to get any challenges, or questions.    :-).
>
> James
> Dec 9, 2018
>
>
>
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